[en] One proposed approach to the overlap/deposition problem for multi-channel electron beams is to place a thin hollow sphere in the overlap region and allow the incoming electrons to form a virtual cathode inside this sphere. The resulting electric field causes ions from the inner surface of the sphere to flow inward radially towards a target. The efficiency of this process is studied analytically and with a 1-D spherical, two-species electrostatic particle code. The maximum possible (power conversion) efficiency is concluded to be about 10 percent. Two-dimensional effects are briefly considered, and angular momentum in particular is found to be a possibly serious limitation